I hope it's ok to pop in suddenly like this? The version I know about where Eliggins shipping comes from is that during the filming of the 1938 Pygmalion, Leslie Howard (who played Higgins) said to GBS "You do realise he's in love with Eliza?" and GBS strongly disagreed. (Wikipedia merely says " Against Shaw's wishes, a happy ending was added, with Eliza fleeing Higgins with Freddy but then returning to Higgins's home (though whether permanently or on her own terms is left deliberately ambiguous"). Personally, I'm quite happy for Eliza to marry Freddy - it's what SHE wants, after all, and while I'm sure there will be problems, I daresay those two crazy kids will overcome them. (I fear Howard's conviction that Eliza should return stems from the tradition that if a male character is in love with a woman, he ends up "getting" her, because heaven forbid female desires should be prioritised over male ones. I also agree with Howard that Higgins is in love with Eliza, I just don't think she's remotely in love with HIM).

None of this means, of course, that Howard was the first Higgins to develop a romantic attachment to Eliza - that anonymous performer in the original run may very well have thrown the bouquet, and GBS's annoyance may have been increased by the fact that he was constantly being told by actors playing Higgins that he and Eliza were in love.